Question 1

Given the points $$(-6,2)$$ and $$(-5,-4)$$, what is the slope $$m of $$the line passing through them?

Accepted Answer

$$m = -6$$

Question 2

Which of the following statements is TRUE about the slope of a vertical line?

Accepted Answer

The slope is undefined.

Question 3

What is the equation of the line in point-slope form passing through $$(3,5)$$ with slope $$m = -2$$?

Accepted Answer

$$y - 5 = -2(x - 3)$$

Question 4

A line passes through the points $$(2,-2)$$ and $$(3,-4). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = -2x + 2$$

Question 5

Which of the following is the general form of a line?

Accepted Answer

$$Ax + By = C$$

Question 6

If a line has $$x-$$intercept $$a$$ and $$y-$$intercept $$b ($$with $$a, b 
eq 0$$), what is its equation in intercept form?

Accepted Answer

$$\frac{x}{a} + \frac{y}{b} = 1$$

Question 7

Two nonvertical lines are perpendicular if and only if:

Accepted Answer

The product of their slopes is $$-1.$$

Question 8

Find the equation of the line passing through $$(0,-4)$$ and $$(3,0) in $$slope-intercept form.

Accepted Answer

$$y = \frac{4}{3}x - 4$$

Question 9

Which of the following lines is parallel to $$y = 3x - 2$$?

Accepted Answer

$$y = 3x + 5$$

Question 10

A vertical line passing through $$(4, -2)$$ has which equation?

Accepted Answer

$$x = 4$$

Question 11

If a line has a slope of $$0$$, which of the following best describes the line?

Accepted Answer

The line is horizontal.

Question 12

Given the equation $$3x - y = 2$$, what is the slope and $$y-$$intercept of the line?

Accepted Answer

Slope: $$3$$, $$y-$$intercept: $$-2$$

Question 13

Which of the following is the equation of a horizontal line passing through $$(3,2)$$?

Accepted Answer

$$y = 2$$

Question 14

If two lines have slopes $$m_1$$ and $$m_2$$ and are parallel, which of the following must be true?

Accepted Answer

$$m_1$$ = $$m_2$$

Question 15

A line passes through $$(1,4)$$ and has a slope of $$-3. $$What is its equation in point-slope form?

Accepted Answer

$$y - 4 = -3(x - 1)$$

Question 16

Which of the following best describes the relationship between a vertical and a horizontal line?

Accepted Answer

They are always perpendicular.

Question 17

Given the tuition data: in 2010, $$T = 31,500$$ and in 2019, $$T = 36,880. $$Let $$t be $$years since 2000. What is the slope $$m of $$the line modeling tuition as a function of $$t$$?

Accepted Answer

$$m = \frac{36,880 - 31,500}{19 - 10} = 598$$

Question 18

A line passes through $$(2,3)$$ and is perpendicular to $$x - 3y = 6. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = 3x - 3$$

Question 19

Which of the following is the correct interpretation of the slope in the context of the tuition application problem?

Accepted Answer

The slope represents the average annual increase in tuition and fees.

Slopes and Equations of Lines in Business Calculus

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